Topological phases have attracted much attention in the context of solid
state materials[1]}, [2]} with the emergence of topological edge
states. They are generalized to higher-order topological phases[3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, where
topological corner states and topological hinge states emerge. Recently,
they are also found in various linear systems such as photonic[14]}, [15]}, [16]}, [17]}, [18]}, [19]}, [20]}, [21]}, [22]}, [23]}, [24]}, [25]}, [26]}, [27]}, [28]}, [29]}, [30]}, [31]}, [32]}, [33]}, acoustic[34]}, [35]}, [36]}, [37]}, [38]}, [39]}, [40]}, [41]}, [42]}, [43]},
mechanical[44]}, [45]}, [46]}, [47]}, [48]}, [49]}, [50]}, [51]}, [52]}, [53]}, [54]}, [55]}, [56]}, [57]}, [58]}, [59]}, [60]}
and electric circuit[61]}, [62]}, [63]}, [64]}, [65]}, [66]}, [67]}, [68]}, [69]}, [70]}, [71]}, [72]}, [73]}, [74]}, [75]}, [76]}
systems. Now, nonlinear topological photonics is an emerging field[20]}, [22]}, [79]}, [80]}, [81]}, where nonlinearity is naturally introduced by the
Kerr effect. Nonlinear higher-order topological phases have been
experimentally studied in photonics[82]}, [83]}. Topological edge
states and topological corner states have been observed in nonlinear systems
just as in linear systems.
